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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::natural::Natural;
use crate::natural::arithmetic::mul::product_of_unsigneds::product_of_unsigneds;
use crate::platform::Limb;
use malachite_base::num::arithmetic::traits::WideningElementProduct;
use malachite_base::num::basic::unsigneds::PrimitiveUnsigned;
use malachite_base::num::conversion::traits::{ConvertibleFrom, WrappingFrom};
use malachite_base::unsigned_vector::UnsignedVector;
impl<T: PrimitiveUnsigned> WideningElementProduct<Natural> for UnsignedVector<T>
where
Limb: ConvertibleFrom<T> + WrappingFrom<T>,
Natural: From<T>,
{
/// Returns the product of the elements of an [`UnsignedVector`] as a [`Natural`], taking the
/// vector by reference.
///
/// The 0-dimensional vector has no elements, and their product is 1. Adjacent elements are
/// multiplied as machine words while their product fits in one, and the resulting words are
/// multiplied in a balanced tree; multiplication stops as soon as an element is zero.
///
/// $$
/// f(v) = \prod_i v_i.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the sum of the numbers of
/// significant bits of the elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::WideningElementProduct;
/// use malachite_base::unsigned_vector::UnsignedVector;
/// use malachite_nz::natural::Natural;
///
/// let v = UnsignedVector::<u64>::from_str("(4294967296, 4294967296, 3)").unwrap();
/// let p: Natural = v.to_widening_element_product();
/// assert_eq!(p.to_string(), "55340232221128654848");
/// let v = UnsignedVector::<u8>::from_str("()").unwrap();
/// let p: Natural = v.to_widening_element_product();
/// assert_eq!(p, 1);
/// ```
///
/// This is equivalent to `_fmpz_ui_vec_prod` from `fmpz_vec/prod.c`, FLINT 3.6.0.
#[inline]
fn to_widening_element_product(&self) -> Natural {
product_of_unsigneds(self.elements.iter().copied())
}
/// Returns the product of the elements of an [`UnsignedVector`] as a [`Natural`], taking the
/// vector by value.
///
/// The 0-dimensional vector has no elements, and their product is 1. Adjacent elements are
/// multiplied as machine words while their product fits in one, and the resulting words are
/// multiplied in a balanced tree; multiplication stops as soon as an element is zero.
///
/// $$
/// f(v) = \prod_i v_i.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the sum of the numbers of
/// significant bits of the elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::WideningElementProduct;
/// use malachite_base::unsigned_vector::UnsignedVector;
/// use malachite_nz::natural::Natural;
///
/// let v = UnsignedVector::<u64>::from_str("(4294967296, 4294967296, 3)").unwrap();
/// let p: Natural = v.into_widening_element_product();
/// assert_eq!(p.to_string(), "55340232221128654848");
/// let v = UnsignedVector::<u8>::from_str("()").unwrap();
/// let p: Natural = v.into_widening_element_product();
/// assert_eq!(p, 1);
/// ```
///
/// This is equivalent to `_fmpz_ui_vec_prod` from `fmpz_vec/prod.c`, FLINT 3.6.0.
#[inline]
fn into_widening_element_product(self) -> Natural {
product_of_unsigneds(self.elements.into_iter())
}
}